EP1815605A1

EP1815605A1 - Method for characterising emitters by the association of parameters related to the same radio emitter

Info

Publication number: EP1815605A1
Application number: EP05801538A
Authority: EP
Inventors: Anne Ferreol
Original assignee: Thales SA
Current assignee: Thales SA
Priority date: 2004-10-27
Filing date: 2005-10-25
Publication date: 2007-08-08
Anticipated expiration: 2025-10-25
Also published as: CN101111998A; FR2877166B1; CA2586008A1; DE602005014002D1; EP1815605B1; US7848748B2; WO2006045803A1; CN101111998B; ATE429079T1; FR2877166A1; US20090305720A1

Abstract

The invention relates to a method for characterising at least one emitter and/or at least one parameter associated with an emitter, using a receiving station comprising a device which is adapted in such a way as to measure, over a period of time, a set of K parameters depending on the emitters associated with vectors ?<SUB>K</SUB> representative of the emitters for 1=k=K. The inventive method comprises a parameter extraction step wherein the parameters associated with each emitter are regrouped by emitter, by means of an independent component analysis technique.

Description

METHOD FOR CHARACTERIZING TRANSMITTERS BY ASSOCIATING PARAMETERS RELATING TO A SAME RADIO-ELECTRIC TRANSMITTER

The invention relates in particular to a method of passive location of transmitters, fixed or mobile, on the ground. The objective is in particular to determine the position of one or more transmitters on the ground from a mobile reception system.

It also applies for configurations where the transmitters are at altitude and the ground receiving system.

The combination of parameters also makes it possible to characterize a transmitter by its signal-to-noise ratio. We can also characterize an EVF

(Frequency evasion) by its durations stages, its frequencies of appearance and its direction of arrival. It is also possible to characterize a modulation by identifying for example its amplitude and phase states.

FIG. 1 illustrates an airborne location with a mobile reception system, the transmitter 1 is at the position (xo.yo.zo), the carrier 2 at the instant fc is at the position (x _k , yk, Zk) and sees the emitter 1 under the incidence (θ (λ, xo, yo, zo), Δ (&, x _o , yo, zo)). The angles θ (f, x _o , y _o , z _o ) and Δ (f, x _o , y _o , z _o ) evolve over time and depend on the position of the transmitter as well as the trajectory of the reception system . The angles θ (f, x _o , y _o , z _o ) and Δ (f, x _o , y _o , z _o ) are identified by means of a network of N antennas that can be fixed under the carrier as shown in FIG. .

The antennas Ai of the network receive the sources with a phase and an amplitude depending on the angle of incidence of the sources as well as the position of the antennas.

Antenna processing techniques generally exploit the spatial diversity of sources (or transmitters): use of the spatial position of network antennas to better exploit differences in incidence and distance from sources. Antenna processing is divided into two main areas of activity: 1-Spatial filtering, illustrated in FIG. 3, which aims to extract either the modulated signals s _m (t) or the symbols contained in the signal (demodulation). This filtering consists of combining the signals received on the sensor network in order to form an optimal reception antenna for one of the sources. Spatial filtering can be blind or cooperative.

It is cooperative when there is knowledge a priori on the signals emitted (directions of arrival, sequences of symbols, ...) and it is blind in the opposite case. It is used for blind source separation, adapted filtering on arrival direction (beam forming) or on replicas, the multi-sensor MODEM (demodulation), etc.

2-The estimation of the parameters of the transmitters aims to determine various parameters such as: their Doppler frequencies, their bit rates, their modulation indices, their positions (x _m , ym), their incidences (θ _m , Δ _m ) and their director vectors a (θ _m , Δ _m ) (response of the sensor array to a source of direction (θ _m , Δ _m )) etc.

In this field, there are for example direction finding and blind identification methods:

The aim of the direction finding is to determine the incidences θ (f, x _m , y _m , z _m ) in 1 D or the couple of incidences (θ (f, x _m , y _m , z _m ), Δ (f, x _m , y _m , z _m )) in 2D. For this, direction finding algorithms use observations from antennas or sensors. When the waves of all transmitters propagate in the same plane, it suffices to apply a 1 D direction finding, in other cases, a 2D direction finding.

The purpose of blind identification methods (ICA) is to determine the direction vectors a (θ _m , Δ _m ) of each of the emitters.

Prior art localization techniques generally use histogram techniques to group the parameters. However, these techniques have the disadvantage of requiring prior knowledge of the standard deviation of the parameters to set the step of the histogram. The invention is based on a new approach consisting in particular to judiciously associate the parameters related to the same transmitter.

The invention relates to a method for characterizing one or more transmitters and / or one or more parameters associated with a transmitter by using a reception station comprising a device adapted to measure over time a set of K parameters depending on the transmitters associated with the transmitters. vectors ή ^ representative of the emitters for 1 <k <K, characterized in that it comprises at least one step of extracting the parameter or parameters of grouping by transmitter the parameters associated with it by means of an analysis technique in independent component.

The process according to the invention has the following advantages:

• It does not require any setting parameters and no prior knowledge about parameter statistics,

• it makes it possible to count the number of transmitters starting from the number of dominant values of a matrix of covariance of the parameters (R _χ J ^: use of the techniques of detection of the number of sources of the direction finding,

• it makes it possible to identify as many parameter vectors (η _m ) as one wishes,

• it allows to use the step of association of the parameters of different nature like the incidence of the sources, their signal-to-noise ratio or their direction vectors,

• it determines the average impact of each incident issuer on measured impacts,

• perform the average location of each incident transmitter from the measured guidance vectors or measured impacts, Extracting the phase states of a modulation from the real and imaginary parts of the signal of a linear modulation,

• to separate Frequency Evasion signals, EVF, from the measurement of bearing times and incidences: an EVF is characterized by a single incidence and a single level.

Other features and advantages of the present invention will emerge more clearly on reading the following description of an exemplary embodiment given by way of illustration and in no way limiting attached to the figures which represent:

• Figure 1 an example of airborne location with a mobile reception system,

• Figure 2 a network of 5 antennas,

FIG. 3 a spatial filtering diagram by beam formation in one direction,

• Figures 4, 5 and 6 an example of the use of the method according to the invention.

The following example is given in relation to FIG. 1, comprising a transmitter 1 to be located using an aircraft 2 equipped with devices making it possible to measure parameters associated with the transmitters and a processor adapted to perform the steps according to the invention.

In the presence of M transmitters, a location system measures, for example over time, a set of K parameters (representative of the emitting sources) characterized by the vectors r \ _k for i <k <K. The vectors η _k are for example composed of the azimuth θ _k and the signal-to-noise ratio SNR ^ of one of the emitters at the instant tk T \ k = [Qk SNR ^] ¹ where ( ^τ ) denotes the transpose of 'a vector.

This vector can also be composed of the director vector a (θk) of one of the sources and its signal-to-noise ratio: r \ k = [a (θ _k ) ^τ SNR ^] ^τ . In a more general way the / c " ³ ™ ³ measurement ή ^ is tainted with an error and is associated with the ^same emitter as follows:% = Αm + θ * r for 1 <k <K and 1 <m < M (1) where βk is the noise vector associated with the / c " ³ ™ ³ measurement and η _m the parameter vector associated with the ^same transmitter.

The invention consists in extracting the M vectors η _m associated with a transmitter m in the middle of K measures ή ^.

Method for identifying the main source parameter vectors

Thanks to the locating system equipping the aircraft or more generally a system performing measurements of parameters, K measures are available. The primary objective of the invention is to identify the

M vectors η _m associated with the M incident transmitters.

For this, the method comprises a first step of transforming the measured vectors ή ^ into vectors f {r \ _k ) of larger size.

For an azimuth direction-finding system θ _k where the vector ή ^ is equal to [SNR / J ^T (azimuth and signal-to-noise ratio), the transformation step consists in carrying out the following bijective transformation:

For an azimuth direction finding system 0 * and a site A _k where the vector representative of the set of parameters K measured for the M transmitters ή = = [Qk Δ _k SNR / c] ^τ the transformation step consists of carrying out the following bijective transformation:

For a direction finding system in the presence of EVF signals whose incidences θ et and bearing times f _k have been measured, the vector ή is written as follows:

Α _k . ⁼ . [θ * T _k ] ^τ . The transformation step of ή ^ consists in carrying out the following bijective transformation:

For a system seeking to extract the phase states of a transmitter from the signal x (kT) of the BPSK, the vector ή ^ is written:

Where 9i (z) and 3 (z) denote the real and imaginary parts of the complex z and T is the symbolic rhythm. In the case of a BPSK emitter with 2 phase states, M = 2 states are in the presence of:

The determination of the vectors Ti ₁ and η _{2 will} make it possible to deduce the phase rotation φ of the BPSK. In this case we can build the following fine vector _k ):

The length of the vector f {r \ _k ) determines the maximum number of identifiable transmitters. In a goniometric-type application estimating the incidences θ or (θ, Δ), it can be said, for example, that this maximum number will not exceed the number of sensors of the network that has allowed direction finding.

From the K> dim (.f (v \ _k )) vectors f [v \ _k ) the method then calculates the following covariance matrix:

R ~ = ^ Σ Wή *) 9flή *)] [/ (ή *) ® / (ή *)] ^H (8)

Λ-k = \ where désigne is the product of Kronecker such that u®v = [u (1) v ^τ u (2) v ^τ ...] and (.) ^H the transposed and the conjugate. This matrix R _^ is also written:

where Rw, is a noise matrix and p _m is the number of vectors / (ή _fc ) associated with the vector f {η _m ).

The matrix R _^ is the covariance matrix of K observations ÂΑ _k ) ®ÂΑ _k ) - From equation (9) it is reduced to the covariance matrix of signatures M transmitters. Knowing that the signatures are all different because the emitters are associated with different parameters, the principal components of the matrix R _^ (eigenvectors associated with the M strongest eigenvalues) define the same space as the M signatures is completely related to the vector space of the M signatures issuers. The rank of the matrix R _^ is thus equal to the number of emitters M.

This rank can be determined from the eigenvalues of this matrix. Thus in the presence of a vector f {r \ _k ) of dimension N, the matrix R _^ is of dimension / V ² X Λ / ² and it is then possible to identify at most N ² emitters.

The method then comprises a step of identifying the transformed vectors / (η _m ) from R _^ and then deriving the vectors of parameters η _m from each of the emitters.

For this, the first operation consists in realizing the decomposition into eigenvectors of the matrix R _^ to obtain its eigenvalues. From the eigenvalues of the matrix, it is possible to determine the number of sources M by applying, for example, the method described in reference [4] or any other method of "counting" which makes it possible to count the number of components main matrix

R _^ . This number in the given example is related to the number M of transmitters. From the M own elements associated with the highest eigenvalues λ _m, we can determine the square root of the matrix R _^ :

AJ ^'2 = E _s Λ _s ^{"/ 2} = B Ω" ^{/ 2} U ^H as B and where diag {..} is a diagonal matrix composed of the elements of {..}, E _s and Λ _s = diag {λi ... λ _M } are respectively composed of eigenvectors and eigenvalues of R _^ associated with M plus strong eigenvalues:

The columns of the matrix B are composed of the signatures / (η _m ) / / (η _m ) of each of the emitters. The matrix U is unitary (U ^H U = I _M where \ _M is the identity matrix of dimension NxN). Knowing that the columns of the square root R _x , ^{1 2} are in the same space as the columns of the matrix B, the matrix U is a basic change matrix. The matrix U is moreover unitary because its columns are orthogonal vectors between them. In the rest of the description, the method will use this property of orthogonality to identify the matrix U. For the identification of U, the method will also use the redundant structure of B which is linked to the Kronecker® product.

The determination of U is done, for example, by exploiting the redundant structure of matrix B, namely:

B with A • ~ AΑM)] ^and (11) where / ή (ηm) is the ri, th component of the vector / (η _m ) of dimension / Vx1.

1/2

Under these conditions the matrix R is composed of Λ / sub-blocks T _n such that:

R 1/2 BU ^H with r "= A Φ" U ^H (12)

The columns of each matrix T _n are in the same vector space as the searched signatures βj \ _m ) of each of the M emitters. The matrices F _n differ by basic change matrices which are equal to a diagonal matrix close to the desired U matrix. These properties of the matrices T _n depend on the redundant structure of the matrix B. Consequently the following matrices Ψy: ψ _y = Γ / Γ _/ = U ΦΓ ¹ Φ ₇ U ^H (13) all have the eigenvector matrix as the matrix U ( ^# denotes the inverse pseudo such that r ^# = (r ^H r) ^"1 r ^H ).

The method uses the unitary character of the matrix U to identify it: The columns of U are orthogonal vectors.

Under these conditions, in order to determine the unitary matrix U, the joint diagonalization of the JADE method described for example in reference [5] of the following matrices or any other method known to those skilled in the art is carried out: Ψ _j , for (l <i <Netj <i) (14)

Once the matrix U is estimated, we can deduce the matrix B to an amplitude by performing from relation (10): Knowing that the ^same column of the matrix B is written b _m = [b _m / ... bmN ^T ] ^τ = / (η _m ) / / (ηm) VPT ^one ^has transformed into the following matrix B _m :

where bmis are vectors of dimensions / Vx1.

Knowing that the 1 ^st component of / (η _m ) is equal to 1, we deduce f (η _m ) from B _m by taking the singular vector e _m from B _m associated with the highest singular value and by performing / (η _m ) = eJe _m (1) where e _m (1) is the first component of the vector e _m . The method performs this normalization because the vectors f {r \ _k ) are always constructed with a first component equal to 1. These steps of construction of f (τ \ k) and of normalization of e _m make it possible to remove the phase ambiguity singular vectors e _m .

From the transformed vectors / (η _m ) we deduce the M main vectors η _m because / (.) Is bijective.

Having identified the M main vectors η _m , the method performs, for example, statistics on the components of each of the vectors. For a location-type application this step makes it possible in particular to give in addition to the average position of the transmitter, a range of error on the estimate of the position.

For example, for the vector η _m = [θ _m SNR _m ] ^τ (1 </ T7 <M), the method determines the statistics of the azimuth θ _m (bias and standard deviation) to give the value of the azimuth in a fork.

The first step consists in determining the set Φ _m of the vectors ή ^ associated with the average vector emitter η _m .

Knowing that : (F ^H F) ^"1 F ^H y (η _w ) (17) where O _L is a zero vector of dimension Lx1.

Thus all components of δ _m are zero except for the _m ^ιeme q j _U j _^unravel. ^ μ f _at j ^. _remar _uence q q _ue | _a filter matrix (F ¹¹ F) ^"1 F ¹¹ is a separator of transmitters: By applying this filter on a signature / (η _m) of the _m ^ιeme em _e tt _{eur is} ule component associated with this transmitter is nonzero.

So to determine the set Φ _{m to} which belongs the vector ή ^, the process uses the property of equation (17) (where the matrix

(F ¹¹ F) ^"1 F ¹¹ aims to separate the transmitters) calculating the vector β * of the equation (14) should be close to δ _m when AΑ _k) ^is associated with the m ^th source.

(F ¹¹ F) ^"1 F ¹¹ AnJ = P, (18)

The vector ή ^ belongs to the set Φ _m of the ^same source if the ^same component > Α. The threshold α is chosen close to 1 (typically α = 0.9).

The steps of the method for constituting the sets Φ _m in the presence of K vectors ή ^ comprise, for example, the following steps:

Step R.1 / c = 1 and initialization of M sets Φ _m to 0 (empty set),

Step R.2 Calculate the vector $ _k using equation (18). Step R.3 Find the component β ^ w) such that: | β / c (/ maχ) |> β / c (/) for t ≠ i _max .

Step R.4 If | β / c (/ _ma χ) |> α then Φ _ιmax = {Φ _imax x \ _k },

Step R.5 k ^ k + λ, Step R.6 If k <K return to step R.2. Once the M sets Φ _m = {r \ _k close to η _m } determined, the method carries out a computation of statistics of the components of the vector η _m for example in Quadratic Mean Error or EQM. The Quadratic Mean Error (EQM) of the / ^e component of η _{m is} written

• \ 2.

EQM _W (O = (ή * (i) - mean _w (0) ² with av _w (0 = *. Σ ή, (i) (19)

where card (Φ _m ) is the cardinal of the set Φ _m and moy _m (/) is the mean value to be close to η _m (/).

In the example of FIGS. 4 and 5, the vector v \ _k = [θ _k ^τ SNR ^] ¹ and the function f {.) Satisfy:

The following Figure 4 shows the distribution of the direction finding pads in space (θ _k , SNR _K ): and Figure 5, the evolution of these pads over time: The method gives for the M = 2 sources:

• 01 = 66.06 ° and SNR ₂ = 27.78 dB

• 0 ₂ = 77.77 ° and SNR ₂ = 28.17 dB

Figures 4 and 5 appear in solid lines the average values estimated by the method. In the example of FIG. 6, the vector v \ _k = [a (θk) ^τ SNR / c] ^τ and the function f {.) Satisfy:

1

Λn _k ) = a (θ.) (21)

SNR _k /(max.(SNR _k ) - min (SNR _k )) In FIG. 6 are represented in dotted lines the coefficients a (θ ^) | and in solid lines the coefficients c _m = | 1 ^H a (θ _m ) | where the director vector a (s _m ) has been deduced from the M vectors s _m estimated by the method. Vector 1 is composed of 1.

The method detected M = 3 source categories.

Figure 6 shows that two of the categories are permanently present while the latter is much more sporadic.

These examples show that the method applies independently to the type of source parameters.

Without departing from the scope of the invention, the method can be applied for arrival directions θ _m , direction vectors a (θ _m ) or signal-to-noise ratios SNR _m . Bibliography

[1] LALBERA, A. FERREOL, P. CHEVALIER and P.COMON. GRETSI 2003, Paris, September 2003, "ICAR, a fast-acting, noise-robust ICA algorithm". [2] LALBERA, A. FERREOL and P. CHEVALIER. ICA2003, Nara (Japan), April 2003, Sixth order blind identification of undetermined mixtures (SIRBI) of sources. [3] P. COMON, Signal Processing, Elsevier, April 1994, vol 36 ", No. 3, pp

287-314, Independent Component Analysis, a new concept ~ ?. [4] O.MICHEL, P.LARZABAL and H.CLERGEOT Detection test of the number of correlated sources for HR methods in antenna processing. GRETSI 91 in Juans les Pins.

[5] J. F. CARDOSO, A. SOULOUMIAC, IEE Proceedings-F, Vol.140, No. 6, pp. 362-370, Dec. 1993. Blind beamforming for non-gaussian signais.

Claims

claims

1 - Method for characterizing one or more transmitters and / or one or more parameters associated with a transmitter by using a reception station comprising a device adapted to measure over time a set of K parameters depending on the transmitters associated with vectors ή representative of the transmitters for 1 <k <K, characterized in that it comprises at least one step of extracting the parameter or parameters of grouping by transmitter the parameters associated with it by means of an independent component analysis technique .

2 - Process according to claim 1 characterized in that the step of combining the parameters for each transmitter M comprises at least the following steps: Step n ° 1 Transform the vectors ή ^ representative of all K parameters for the M emitters into vectors f (v \ _k ) using a bijective function / Q and where the 1 ^st component of f (v \ _k ) is equal to 1, Step n ° 2 determine a covariance matrix R _^ from the vectors f (v \ _k ) and break it down into clean elements, in order to obtain its eigenvalues,

Where R _^ is a matrix linked to the vector space of the M signatures / (η _m ) / / (η _m ) of the emitters.

Step 3 Calculate the rank M of the matrix R _ïΛ from its eigenvalues found in step 2, Step 4 Calculate a square root of R _^ with its M dominant dominant elements: AJ ¹² = E _s Λ _s ^{/ 2} where E _s corresponds to eigenvectors and Λ _s to M have higher eigenvalues, I \

1/2

Step 5 Derive from R _^ matrices T _n following R = BU ^H r, with r _B = A Φ _B U ^H and from T _n calculate ψ, following Ψ _y = T? T _j = U Φf ¹ Φ, U ^H for (1 <i <Λ / ety </), where the columns of each matrix T _n define the same vector space as the signatures / (η _m ) of the M emitters,

Step 6 From the joint diagonalization of Ψq for (1 </ ^ Λ / and j <i) we identify the unit matrix U,

Step 7 Determine the vectors / (η _m ) from the columns b _m of the matrix R _x / ' ² U where U is the unit matrix: Transformation of the column b _m into the matrix B _m according to B _m = [ b _ml ... ^and extracting this matrix of the singular vector e _m associated with the highest singular value to perform / (η _m ) = e _m / e _m (1) with e _m (1) the component of the vector e _m .

Step 8 Apply the inverse transform of the function / Q to derive the vectors η _m .

3 - Process according to claim 2 characterized in that it comprises at least one step of evaluation of the statistics of the components of the vectors η _m found.

4 - Process according to claim 3 characterized in that it comprises a step of evaluating the average and the standard deviation of the incidences of each of the transmitters.

5 - Process according to claim 3 characterized in that it comprises at least the following steps:

• to determine the M sets Φ _m of vectors ή ^ associated with the vector principal η _m . determine the statistics of the components of the vector η _m from the set Φ _m using a method of Square Mean Error.